|
|
A171382
|
|
a(n) = (2*2^n+7*(-1)^n)/3.
|
|
3
|
|
|
3, -1, 5, 3, 13, 19, 45, 83, 173, 339, 685, 1363, 2733, 5459, 10925, 21843, 43693, 87379, 174765, 349523, 699053, 1398099, 2796205, 5592403, 11184813, 22369619, 44739245, 89478483, 178956973, 357913939, 715827885, 1431655763, 2863311533
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
Second binomial transform of a signed version of A005032 preceded by 3.
Inverse binomial transform of A008776 preceded by 3.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = a(n-1)+2*a(n-2) for n > 1; a(0) = 3, a(1) = -1.
a(n) = 2^n-a(n-1) for n > 0; a(0) = 3.
G.f.: (3-4*x)/((1+x)*(1-2*x)).
|
|
MATHEMATICA
|
Nest[Append[#, Last[#]+2#[[-2]]]&, {3, -1}, 40] (* Harvey P. Dale, Apr 07 2011 *)
|
|
PROG
|
(Magma) [ (2*2^n+7*(-1)^n)/3: n in [0..32] ];
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|